Pushing up \(Sp(4,q)\), q odd
type: Item
instance of: scholarly article
title: Pushing up \(Sp(4,q)\), q odd
zbMATH Open document ID: 0636.20011
DOI: 10.1016/0021-8693(88)90101-9
author: U. Meierfrankenfeld
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author handles the pushing-up situation for \(Psp(4,p^ n)\), p odd. Let M be a finite group, p a prime, S a Sylow p-subgroup of M. Assume that no nontrivial characteristic subgroup of S is normal in M and \((M/O_ p(M))/\Phi (M/O_ p(M))\cong PSp(4,p^ n)\), p odd. Set \(\tilde M=O^ p(M)\) and \(V=O_ p(\tilde M)\). Assume \(O_ p(M)=1\). Then either \(\tilde M\cong PSp(4,p^ n)\) or \(\tilde M/V\cong Sp(4,p^ n)\) and V is the natural \(Sp(4,p^ n)\)-module. As in his papertreating the even characteristic [ibid. 112, 430-466 (1988; reviewed above)] the author uses the amalgam-method to prove his result. But by lack of strange examples the proof is much easier.
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 4036054
zbMATH Keywords: symplectic groups
zbMATH Keywords: pushing-up
zbMATH Keywords: Psp
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: amalgam-method
reviewed by: Gernot Stroth
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90101-9
OpenAlex ID: W1972958735
cites work: A Pair of Characteristic Subgroups for Pushing-Up in Finite Groups
cites work: Automorphisms of trivalent graphs
cites work: Q5577154
cites work: Pushing up Sp(4,2 k)
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description: scientific article; zbMATH DE number 4036054